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International Journal of Mathematics and Mathematical Sciences
Volume 2004, Issue 24, Pages 1239-1253
http://dx.doi.org/10.1155/S0161171204306186

Fuzzy multiply positive implicative hyper BCK-ideals of hyper BCK-algebras

Department of Mathematics, Hubei Institute for Nationalities, Hubei Province, Enshi 445000, China

Received 23 June 2003

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider the fuzzification of the notion of fuzzy multiply positive implicative hyper BCK-ideals of BCK-algebras and then some related results are obtained. Using the concept of level subsets, we give a characterization of a fuzzy multiply positive implicative hyper BCK-ideal. We state a relation between a fuzzy hyper BCK-ideal and a fuzzy multiply positive implicative hyper BCK-ideal. Moreover, we introduce the notions of Noetherian hyper BCK-algebras and hyper homomorphisms of hyper BCK-algebras and investigate some related properties. Finally, we introduce the concept of hyper normalization of hyper BCK-algebras and discuss related properties.